# How do you differentiate f(x) = (x+sqrtx)^(3/2)  using the chain rule?

Nov 25, 2016

The answer is $= \frac{3}{2} {\left(x + \sqrt{x}\right)}^{\frac{1}{2}} \cdot \left(1 + \frac{1}{2 \sqrt{x}}\right)$

#### Explanation:

We use $\left({u}^{n}\right) ' = n {u}^{n - 1}$

The derivative of $f \left(x\right)$ is

$f ' \left(x\right) = \frac{3}{2} {\left(x + \sqrt{x}\right)}^{\frac{1}{2}} \left(x + \sqrt{x}\right) '$

$= \frac{3}{2} {\left(x + \sqrt{x}\right)}^{\frac{1}{2}} \cdot \left(1 + \frac{1}{2 \sqrt{x}}\right)$